Scala analysis: balasept-under
5.7.13.15.21 tuning based on a single Balasept sequence
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 277/240 248.221885 3: 97/80 333.581697 4: 13/10 454.213948 tridecimal semi-diminished fourth 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 97/60 831.626696 9: 26/15 952.258947 tridecimal semi-augmented sixth 10: 28/15 1080.557192 grave major seventh 11: 39/20 1156.168949 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 21/20 84.4672 minor semitone 2: 277/252 163.7547 3: 291/277 85.3598 4: 104/97 120.6323 5: 40/39 43.8311 tridecimal minor diesis 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 97/90 129.6717 9: 104/97 120.6323 10: 14/13 128.2982 2/3-tone 11: 117/112 75.6118 12: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 1 117/112 75.612 cents 1: 2 21/20 84.467 cents minor semitone 1: 1 291/277 85.360 cents 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 104/97 120.632 cents 1: 1 14/13 128.298 cents 2/3-tone 1: 1 97/90 129.672 cents 1: 1 277/252 163.755 cents 2: 1 15/14 119.443 cents major diatonic semitone 2: 2 14/13 128.298 cents 2/3-tone 2: 1 320/291 164.463 cents 2: 2 9/8 203.910 cents major whole tone 2: 1 312/277 205.992 cents 2: 1 277/240 248.222 cents 2: 1 112/97 248.930 cents 2: 2 97/84 249.115 cents 2: 1 52/45 250.304 cents 3: 1 9/8 203.910 cents major whole tone 3: 2 15/13 247.741 cents tridecimal 5/4-tone 3: 1 112/97 248.930 cents 3: 1 320/277 249.823 cents 3: 1 277/234 292.053 cents 3: 1 117/97 324.542 cents 3: 2 97/80 333.582 cents 3: 2 26/21 369.747 cents 3: 1 56/45 378.602 cents septimal narrow major third 4: 1 63/52 332.208 cents 4: 1 336/277 334.290 cents 4: 1 277/224 367.665 cents 4: 2 120/97 368.373 cents 4: 2 97/78 377.413 cents 4: 1 80/63 413.578 cents wide major third 4: 3 13/10 454.214 cents tridecimal semi-diminished fourth 4: 1 4/3 498.045 cents perfect fourth 5: 1 126/97 452.840 cents 5: 1 291/224 453.025 cents 5: 1 360/277 453.733 cents 5: 1 277/208 495.963 cents 5: 6 4/3 498.045 cents perfect fourth 5: 1 39/28 573.657 cents 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 160/117 541.876 cents 6: 1 39/28 573.657 cents 6: 1 291/208 581.323 cents 6: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 388/277 583.405 cents 6: 1 277/194 616.595 cents 6: 2 10/7 617.488 cents Euler's tritone 6: 1 416/291 618.677 cents 6: 1 56/39 626.343 cents 6: 1 117/80 658.124 cents 7: 1 10/7 617.488 cents Euler's tritone 7: 1 56/39 626.343 cents 7: 6 3/2 701.955 cents perfect fifth 7: 1 416/277 704.037 cents 7: 1 277/180 746.267 cents 7: 1 448/291 746.975 cents 7: 1 97/63 747.160 cents 8: 1 3/2 701.955 cents perfect fifth 8: 3 20/13 745.786 cents tridecimal semi-augmented fifth 8: 1 63/40 786.422 cents narrow minor sixth 8: 2 156/97 822.587 cents 8: 2 97/60 831.627 cents 8: 1 448/277 832.335 cents 8: 1 277/168 865.710 cents 8: 1 104/63 867.792 cents 9: 1 45/28 821.398 cents septimale wide minor sixth 9: 2 21/13 830.253 cents 9: 2 160/97 866.418 cents 9: 1 194/117 875.458 cents 9: 1 468/277 907.947 cents 9: 1 277/160 950.177 cents 9: 1 97/56 951.070 cents 9: 2 26/15 952.259 cents tridecimal semi-augmented sixth 9: 1 16/9 996.090 cents Pythagorean minor seventh 10: 1 45/26 949.696 cents 10: 2 168/97 950.885 cents 10: 1 97/56 951.070 cents 10: 1 480/277 951.778 cents 10: 1 277/156 994.008 cents 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 291/160 1035.537 cents 10: 2 13/7 1071.702 cents 16/3-tone 10: 1 28/15 1080.557 cents grave major seventh 11: 1 504/277 1036.245 cents 11: 1 180/97 1070.328 cents 11: 1 13/7 1071.702 cents 16/3-tone 11: 2 97/52 1079.368 cents 11: 1 28/15 1080.557 cents grave major seventh 11: 1 554/291 1114.640 cents 11: 2 40/21 1115.533 cents acute major seventh 11: 1 224/117 1124.388 cents 11: 2 39/20 1156.169 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.54545 = 94/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 248.2 333.6 454.2 498.0 582.5 702.0 831.6 952.3 1080.6 1156.2 1200.0 84.5 : 163.8 249.1 369.7 413.6 498.0 617.5 747.2 867.8 996.1 1071.7 1115.5 1200.0 248.2 : 85.4 206.0 249.8 334.3 453.7 583.4 704.0 832.3 907.9 951.8 1036.2 1200.0 333.6 : 120.6 164.5 248.9 368.4 498.0 618.7 747.0 822.6 866.4 950.9 1114.6 1200.0 454.2 : 43.8 128.3 247.7 377.4 498.0 626.3 702.0 745.8 830.3 994.0 1079.4 1200.0 498.0 : 84.5 203.9 333.6 454.2 582.5 658.1 702.0 786.4 950.2 1035.5 1156.2 1200.0 582.5 : 119.4 249.1 369.7 498.0 573.7 617.5 702.0 865.7 951.1 1071.7 1115.5 1200.0 702.0 : 129.7 250.3 378.6 454.2 498.0 582.5 746.3 831.6 952.3 996.1 1080.6 1200.0 831.6 : 120.6 248.9 324.5 368.4 452.8 616.6 702.0 822.6 866.4 950.9 1070.3 1200.0 952.3 : 128.3 203.9 247.7 332.2 496.0 581.3 702.0 745.8 830.3 949.7 1079.4 1200.0 1080.6: 75.6 119.4 203.9 367.7 453.0 573.7 617.5 702.0 821.4 951.1 1071.7 1200.0 1156.2: 43.8 128.3 292.1 377.4 498.0 541.9 626.3 745.8 875.5 996.1 1124.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 163.7547 cents 3601/3360, 119.9236 cents 40/39, 43.8311 cents 2: 119.4428 .. 250.3039 cents 728/675, 130.8611 cents 270/277,-44.3119 cents 3: 203.9100 .. 378.6022 cents 448/405, 174.6922 cents 405/416,-46.3939 cents 4: 332.2082 .. 498.0450 cents 208/189, 165.8368 cents 405/416,-46.3939 cents 5: 452.8405 .. 582.5122 cents 97/90, 129.6717 cents 189/194,-45.2045 cents 6: 541.8761 .. 658.1239 cents 13689/12800, 116.2479 cents 800/819,-40.6361 cents 7: 617.4878 .. 747.1595 cents 97/90, 129.6717 cents 800/819,-40.6361 cents 8: 701.9550 .. 867.7918 cents 208/189, 165.8368 cents 189/194,-45.2045 cents 9: 821.3978 .. 996.0900 cents 448/405, 174.6922 cents 405/416,-46.3939 cents 10: 949.6961 .. 1080.5572 cents 728/675, 130.8611 cents 405/416,-46.3939 cents 11: 1036.2453 .. 1156.1689 cents 3601/3360, 119.9236 cents 270/277,-44.3119 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 277/252, 163.7547 cents Average / Smallest step : 2.281488 Largest / Average step : 1.637547 Largest / Smallest step : 3.736043 Median interval of one step : 102.40131 cents, amount: 0 Least squares average step : 103.76041 cents, oct.: 1245.12497 cents Scale is not proper Step pattern alph. order: ABCDEAFGDHIE Step pattern size order : CIDFACEHFGBA Scale is not a Constant Structure Scale diversity : 1.426464 Lumma stability : 0.073052 Lumma impropriety factor : 0.371567 Rothenberg efficiency : 0.265909 redundancy: 0.734091 Efficiency x scale size : 3.190909 Number of different interval sizes : 80 = 7.27273 / class Number of one step interval sizes : 9 Highest interval variety : 10 Mean interval variety : 8.54545 = 94/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 9409/9408, 0.1840 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 8, average 702.2153 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 277 Odd number limit : 291 (O: 291 U: 291) Highest odd numerator or denominator: 277 Scale harmonicity : 0.019931 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 29340948, 24.8064 octaves, 7676342106.967 Hz. Exponens Consonantiae : 7.041828E+09, 32.71330 octaves Euler's gradus suavitatis : 405 Sum of Mann's harmonic distance : 542.5, average 45.20833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.59477, average 1.21623 Sum of Tenney's harmonic distance : 29.02351, average 2.41863 Vogel's harmonic complexity : 51.16667 Wille's k value : 145 Wilson's harmonic complexity : 405 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 232.21765, average 2.97715 Lattice compactness (without 2's) : 117.18150, average 1.50233 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.83333 22 1 3: -1 .. 1 -0.16667 8 2 5: -1 .. 0 -0.75000 9 7: 0 .. 1 0.25000 3 3 13: 0 .. 1 0.25000 3 3 97: 0 .. 1 0.16667 2 2 277: 0 .. 1 0.08333 1 1 Average exponent except 2's :-2 / 12 =-0.16667 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is weakly epimorphic with val: <12 19 27 33 42 79 96| Scale is weakly epimorphic with val: <12 19 28 34 43 80 97| Scale is weakly epimorphic with val: <12 19 29 32 45 78 98| Scale is weakly epimorphic with val: <12 19 29 33 44 78 98| Scale is weakly epimorphic with val: <12 20 27 33 42 80 96| Scale is weakly epimorphic with val: <12 20 27 33 46 80 96| Scale is weakly epimorphic with val: <12 20 27 34 45 80 96| Scale is weakly epimorphic with val: <12 20 29 34 43 80 96| Scale is weakly epimorphic with val: <12 20 29 35 42 80 96| Scale is weakly epimorphic with val: <12 20 29 35 46 80 96|
FIT/MODE
12: 0 2 1 1 0 1 1 2 1 1 1 1 N T3 SD: 66.9070 c. M: 101.9550 c. 13: 0 2 1 1 1 1 1 1 2 1 1 1 N D3 SD: 59.8678 c. M: 93.1652 c. 14: 1 2 1 1 1 1 1 2 1 2 1 0 N SD: 21.3235 c. M:-43.8311 c. 18: 1 3 1 2 0 2 1 2 2 2 1 1 N SD: 21.2539 c. M: 35.2883 c. 19: 1 3 1 2 1 1 2 2 2 2 1 1 N SD: 12.2337 c. M: 21.3093 c. 24: 2 3 2 2 1 2 2 3 2 3 1 1 N SD: 11.5613 c. M:-19.4428 c. 26: 2 3 2 3 1 2 2 3 3 2 2 1 N SD: 11.8248 c. M: 19.0187 c. 28: 2 4 2 3 1 2 2 3 3 3 2 1 N SD: 12.1458 c. M:-17.4878 c. 29: 2 4 2 3 1 2 3 3 3 3 2 1 N SD: 2.4102 c. M: 4.6951 c. 82: 6 11 6 8 3 6 8 9 8 9 5 3 N SD: 1.8807 c. M:-3.3377 c. 101: 7 14 7 10 4 7 10 11 10 11 6 4 N SD: 1.6004 c. M: 3.6937 c. 111: 8 15 8 11 4 8 11 12 11 12 7 4 N SD: 0.9801 c. M:-2.0193 c. 140: 10 19 10 14 5 10 14 15 14 15 9 5 N SD: 0.7019 c. M:-1.2471 c. 241: 17 33 17 24 9 17 24 26 24 26 15 9 N SD: 0.5984 c. M: 1.2216 c. 270: 19 37 19 27 10 19 27 29 27 29 17 10 N SD: 0.5612 c. M: 1.1478 c. 299: 21 41 21 30 11 21 30 32 30 32 19 11 N SD: 0.6247 c. M: 1.0884 c. 352: 25 48 25 35 13 25 35 38 35 38 22 13 N SD: 0.5660 c. M: 1.1226 c. 359: 25 49 26 36 13 25 36 39 36 38 23 13 N SD: 0.6148 c. M: 0.9017 c. 381: 27 52 27 38 14 27 38 41 38 41 24 14 N SD: 0.4895 c. M: 1.0778 c. 410: 29 56 29 41 15 29 41 44 41 44 26 15 N SD: 0.4857 c. M: 1.0394 c. 460: 32 63 33 46 17 32 46 50 46 49 29 17 N SD: 0.4924 c. M: 0.9889 c. 465: 33 63 33 47 17 33 46 50 47 50 29 17 N SD: 0.4705 c. M:-0.7331 c. 470: 33 64 34 47 17 33 47 51 47 50 30 17 N SD: 0.4498 c. M:-0.8864 c. 489: 34 67 35 49 18 34 49 53 49 52 31 18 N SD: 0.4994 c. M: 1.0316 c. 494: 35 67 35 50 18 35 49 53 50 53 31 18 N SD: 0.4371 c. M: 0.8575 c. 525: 37 72 37 53 19 37 52 57 53 56 33 19 N SD: 0.4959 c. M:-0.9210 c. 528: 37 72 38 53 19 37 53 57 53 56 34 19 N SD: 0.4934 c. M: 1.0117 c. 542: 38 74 39 54 20 38 54 59 54 58 34 20 N SD: 0.3967 c. M:-0.8456 c. 554: 39 76 39 56 20 39 55 60 56 59 35 20 N SD: 0.4381 c. M:-0.8756 c. 566: 40 77 40 57 21 40 56 61 57 61 35 21 N SD: 0.4684 c. M: 0.7195 c. 571: 40 78 41 57 21 40 57 62 57 61 36 21 N SD: 0.3402 c. M:-0.5975 c. 600: 42 82 43 60 22 42 60 65 60 64 38 22 N SD: 0.3291 c. M: 0.5572 c. 682: 48 93 49 68 25 48 68 74 68 73 43 25 N SD: 0.3207 c. M:-0.7292 c. 684: 48 93 49 69 25 48 68 74 69 73 43 25 N SD: 0.3071 c. M: 0.8535 c. 706: 50 96 50 71 26 50 70 76 71 76 44 26 N SD: 0.3644 c. M:-0.5186 c. 711: 50 97 51 71 26 50 71 77 71 76 45 26 N SD: 0.2883 c. M:-0.5955 c. 766: 54 104 55 77 28 54 76 83 77 82 48 28 N SD: 0.2699 c. M: 0.7023 c. 795: 56 108 57 80 29 56 79 86 80 85 50 29 N SD: 0.2209 c. M: 0.6747 c. 824: 58 112 59 83 30 58 82 89 83 88 52 30 N SD: 0.2057 c. M: 0.6491 c. 867: 61 118 62 87 32 61 86 94 87 93 54 32 N SD: 0.2643 c. M: 0.4710 c. 882: 62 120 63 89 32 62 88 95 89 94 56 32 N SD: 0.2629 c. M: 0.6028 c. 896: 63 122 64 90 33 63 89 97 90 96 56 33 N SD: 0.2094 c. M: 0.4540 c. 925: 65 126 66 93 34 65 92 100 93 99 58 34 N SD: 0.1797 c. M: 0.4381 c. 954: 67 130 68 96 35 67 95 103 96 102 60 35 N SD: 0.1811 c. M: 0.4231 c. 983: 69 134 70 99 36 69 98 106 99 105 62 36 N SD: 0.2080 c. M: 0.4091 c. 1007: 71 137 72 101 37 71 100 109 101 108 63 37 N SD: 0.1885 c. M: 0.3569 c. 1036: 73 141 74 104 38 73 103 112 104 111 65 38 N SD: 0.1412 c. M: 0.3454 c. 1065: 75 145 76 107 39 75 106 115 107 114 67 39 N SD: 0.1208 c. M: 0.3346 c. 1094: 77 149 78 110 40 77 109 118 110 117 69 40 N SD: 0.1339 c. M: 0.3243 c. 1123: 79 153 80 113 41 79 112 121 113 120 71 41 N SD: 0.1693 c. M: 0.3145 c. 1147: 81 156 82 115 42 81 114 124 115 123 72 42 N SD: 0.1718 c. M:-0.2756 c. 1176: 83 160 84 118 43 83 117 127 118 126 74 43 N SD: 0.1396 c. M: 0.2627 c. 1205: 85 164 86 121 44 85 120 130 121 129 76 44 N SD: 0.1307 c. M: 0.2551 c. 1234: 87 168 88 124 45 87 123 133 124 132 78 45 N SD: 0.1459 c. M: 0.2478 c. 1479: 104 202 105 149 54 104 147 160 149 158 93 54 N SD: 0.1249 c. M:-0.2765 c. 1508: 106 206 107 152 55 106 150 163 152 161 95 55 N SD: 0.1193 c. M:-0.2609 c. 1537: 108 210 109 155 56 108 153 166 155 164 97 56 N SD: 0.1307 c. M:-0.2459 c. 1580: 111 216 112 159 58 111 157 171 159 169 99 58 N SD: 0.1445 c. M: 0.2196 c. 1590: 112 217 113 160 58 112 158 172 160 170 100 58 N SD: 0.1068 c. M:-0.1975 c. 1619: 114 221 115 163 59 114 161 175 163 173 102 59 N SD: 0.0874 c. M:-0.1808 c. 1648: 116 225 117 166 60 116 164 178 166 176 104 60 N SD: 0.0879 c. M:-0.1682 c. 1720: 121 235 122 173 63 121 171 186 173 184 108 63 N SD: 0.0883 c. M:-0.1502 c. 1730: 122 236 123 174 63 122 172 187 174 185 109 63 N SD: 0.1024 c. M:-0.1571 c. 1749: 123 239 124 176 64 123 174 189 176 187 110 64 N SD: 0.0779 c. M:-0.1486 c. 1860: 131 254 132 187 68 131 185 201 187 199 117 68 N SD: 0.0620 c. M:-0.1652 c. 1889: 133 258 134 190 69 133 188 204 190 202 119 69 N SD: 0.0569 c. M:-0.1635 c. 2219: 156 303 158 223 81 156 221 240 223 237 140 81 N SD: 0.0629 c. M: 0.1049 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x 5 x x x 6 S SD: 17.5773 cents 4 x x 5 x x x 6 x 7 x x 8 S SD: 13.8183 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.5761 cents 6 x 7 x x 8 x 9:10 x 11 x 12 S SD: 10.6739 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 9.8338 cents 8 x 9:10 x x 11:12:13:14:15 x 16 S SD: 9.7871 cents 9 x 10:11 x 12:13:14:15:16:17 x 18 S SD: 14.2882 cents 10:11 x 12:13 x 14:15:16:17:19 x 20 SD: 10.6568 cents 11:12:13 x 14:15 x 17:18:19 x 21:22 SD: 12.8688 cents 12:13:14:15 x 16:17:18:19:21:22:23:24 SD: 9.0522 cents 13:14:15:16:17 x 18:20:21:23:24:25:26 SD: 7.7084 cents 14:15:16:17:18:19:20:21:23:24:26:27:28 SD: 6.2544 cents 15:16:17:18 x 20:21:23:24:26:28:29:30 SD: 5.7856 cents 16:17:18:19:21 x 22:24:26:28:30:31:32 SD: 6.7229 cents 17:18:20:21:22:23:24:26:27:29:32:33:34 SD: 6.6494 cents 18:19:21:22:23:24:25:27:29:31:34:35:36 SD: 4.0029 cents 19:20:22:23:25 x 27:29:31:33:35:37:38 SD: 4.8661 cents 20:21:23:24:26:27:28:30:32:35:37:39:40 SD: 3.3963 cents 22:23:25:27 x 29:31:33:36:38:41:43:44 SD: 4.3004 cents 23:24:27:28:30:31:32:35:37:40:43:45:46 SD: 3.9924 cents 24:25:28:29:31:32:34:36:39:42:45:47:48 SD: 3.3176 cents 25:26:29:30 x 33:35:38:40:43:47:49:50 SD: 4.2948 cents 26:27:30:32:34:35:36:39:42:45:49:51:52 SD: 3.8806 cents 27:28:31:33:35:36:38:41:44:47:50:53:54 SD: 3.5962 cents 32:34:37:39:42:43:45:48:52:55:60:62:64 SD: 3.2283 cents 33:35:38:40:43:44:46:50:53:57:62:64:66 SD: 2.7331 cents 37:39:43:45:48:49:52:56:60:64:69:72:74 SD: 2.2183 cents 38:40:44:46:49:51:53:57:61:66:71:74:76 SD: 2.0378 cents 44:46:51:53:57:59:62:66:71:76:82:86:88 SD: 1.9906 cents 46:48:53:56:60:61:64:69:74:80:86:90:92 SD: 1.9719 cents 52:55:60:63:68:69:73:78:84:90:97:101:104 SD: 1.6976 cents 57:60:66:69:74:76:80:86:92:99:106:111:114 SD: 1.3235 cents 60:63:69:73:78:80:84:90:97:104:112:117:120 SD: 0.7192 cents 104:109:120:126:135:139:146:156:168:180:194:203:208 SD: 0.7040 cents 117:123:135:142:152:156:164:176:189:203:218:228:234 SD: 0.6106 cents 123:129:142:149:160:164:172:185:199:213:230:240:246 SD: 0.5808 cents 136:143:157:165:177:181:190:204:220:236:254:265:272 SD: 0.5388 cents 156:164:180:189:203:208:218:234:252:270:291:304:312 SD: 0.4620 cents 160:168:185:194:208:213:224:240:259:277:299:312:320 SD: 0.4573 cents 180:189:208:218:234:240:252:270:291:312:336:351:360 SD: 0.2397 cents 240:252:277:291:312:320:336:360:388:416:448:468:480 SD: 0.0000 cents